I was playing as sion and everything was fine until I fought Fiddle. I don't know if this was a weird interaction with fiddle but after the fight I couldn't use my Q or R but W and E worked fine. They made the little failed input noise but nothing happened (they weren't on cooldown). I got myself killed twice and the abilities still didn't work. I ended up reconnecting and then they were useable again.
Try doing alt + Q then alt + R. Happened once to me and this is the solution I found that worked.
Word from Riot is that they've hopefully pinned down what made this happen during matches, and should be fixed in the next patch. Varus, Vi, Xerath, and Sion all suffered from it.
I haven't had the problem though since I put all my abilities on Smart Cast, fixed it automatically in a match one time and haven't seen the problem since.
force quitting the game, and re-loading did it for me. Lost about 30 seconds of time, but didn't lose the game, because sion without QR is useless.
